Here we describe the logical design and testing of a general-purpose neurocomputer, AMNIAC. It may be thought of as a programmable neural network that can simulate arbitrary SIMD and MIMD machines of practical interest (modeled as cellular automata, neural networks, or arbitrary automata networks). AMNIAC is purely bitwise (amnesic), i.e., requires no local memory or registers, other than short memory just long enough for a clock cycle. We discuss software serial and massively parallel simulations of AMNIAC as (a) tests of the logical design; and (b) benchmarks for evaluation of the trade-off between its universality and memory advantage versus overhead cost of mapping and speed. Theoretical applications of the design are given. A 3D SIMD v...